Strong-coupling expansion of chiral models

Abstract

The strong-coupling character expansion of lattice models is reanalyzed in the perspective of its complete algorithmization. The geometric problem of identifying, counting, and grouping together all possible contributions is disentangled from the group-theoretical problem of weighting them properly. The first problem is completely solved for all spin models admitting a character-like expansion and for arbitrary lattice connectivity. The second problem is reduced to the evaluation of a class of invariant group integrals defined on simple graphs. Since these integrals only depend on the global symmetry of the model, results obtained for principal chiral models can be used without modifications in lattice gauge theories. By applying the techniques and results obtained we study the two-dimensional principal chiral models on the square and honeycomb lattice. These models are a prototype field theory sharing with QCD many properties. Strong-coupling expansions for Green's functions are derived up to 15th and 20th order respectively. Large-$N$ and $N=\infty$ results are presented explicitly. Related papers are devoted to a discussion of the results.

47 pages (including 6 figures), latex (revtex + eepic macros), PostScript available at ftp://ftp.difi.unipi.it/pub/campo/preprints/ (Revised: LaTeX problems in figures fixed)

References in corpus (2)

• Two dimensional SU(N) x SU(N) chiral models on the lattice
• Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function

Cited by in corpus (11)

• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Finite Size Effects in Thermal Field Theory
• Large-N phase transition in lattice 2-d principal chiral models
• On the evaluation of universal non-perturbative constants in O(N) sigma models
• A strong-coupling analysis of two-dimensional O(N) sigma models with $N\ge 3$ on square, triangular and honeycomb lattices
• Twisted Eguchi-Kawai Reduced Chiral Models
• Exact duality transformations for sigma models and gauge theories
• Critical Behavior of Simplicial Chiral Models
• Strong coupling analysis of the large-N 2-d lattice chiral models
• Perturbative study of large $N$ principal chiral model with twisted reduction
• An Approximate Large $N$ Method for Lattice Chiral Models